Solving Arc Problem with Given Values & Co-ordinates

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In summary, the conversation is about a geometry problem where the person is trying to set out an arc for a wall. They have been given all the necessary values but do not know how to use them to find the Y value of the arc after walking 10m in the X-axis. However, the problem is indeterminate without more information, such as the type of arc, Y1 or Y2 values, and the orientation of the blue line in the diagram. The person provides more specific information, including the fact that the arc is circular and the green and blue lines are tangent to it. Possible solutions are discussed, including finding the equation of the circle and using the given points to solve for the unknowns. It is also mentioned that the
  • #1
tomtomtom1
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Hello all

I was hoping someone could help me with a geometry problem.

Firstly this is not a homework question – this is work related I am just not very good with Maths.

I have been asked to set out an arc for a wall. I have been given all the values I need but I do not know how the values were work out.

The problem is this:-

I have an arc with a radius and start co-ordinates and end co-ordinates, there are straight lines that are tangent to the arc on either side.

If I was standing on the start of the arc and walked 10m in the x-axis what would the Y value be to the arc.

Hope that makes sense.

I have attached a sketch to help get my point across. I really want to know how it is worked out.

Thanks
 

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  • #2
Problem is indeterminate given that information. The most significant piece of information not provided is what KIND of arc is it? I guess we can assume circular with radius R, but asking people to help solve a problem based on assumptions can be a waste of time. Also, you HAVE to specify at least one of Y1, Y2. Also, is the blue line supposed to be vertical?

You should post your image up and down, not sideways.
 
  • #3
I see the confusion.

The idea was to find a generic way of getting the results but by stating R=2000 I realize the issue the problem it has caused.

So to be specific:-

The green line is straight and tangent to the arc at co-ordinates 860,102.800.
The arc has a radius of 2000 & is circular.
The blue line is straight and tangent to the arc at co-ordinates 900, 103.202.
The points are all in a flat plane and is represented in a standard Cartesian coordinates system.
 
  • #4
So X1 is both 200 and 860 and X2 is both 230 and 900. You have lost me completely.
 
  • #5
X1= 860, y1= 102.800
x2 = 900, y2 = 103.202
 
  • #6
tomtomtom1 said:
X1= 860, y1= 102.800
x2 = 900, y2 = 103.202

Yes, I heard that the first time. So what are the X axis indicators on the chart itself?
 
  • #7
I have redone the sketch, hopefully this will clear things up
 

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  • #8
OK, NOW I believe that you have a full problem statement that probably has a solution. I'm hoping, for your sake that there is an easier way than what I have to find the solution, but here's one way:

You have two points (X1,Y1 and X4,Y4) which will give you the slope of the line between them

You can easily get the midpoint between the two

Now you have a point and the inverse of the slope, which gives you the equation of a line.

You have one point on the line and you know that there is another point on the line that is the center of the circle (but you don't know how far away it is) and you know the radius of the circle

From that you can construct a rather messy equation for the circle that will have unknowns in it

You have two points on the circle and an equation for the circle.

The SHOULD, I think, be enough to solve for the unknows, thus giving you the equation of the circle.

From there you just plug in the X values and solve for the Y values.

Good luck with that.

The green and blue lines, by the way, are totally irrelevant and can be erased. They have no bearing on the solution.

Also, based on the numbers you gave for X1,Y1 and X2, Y2 (which I assume is not X4,Y4), your drawing is massively out of scale so I'm dubious about this actually being a real-world problem.
 
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  • #9
tomtomtom1 said:
The blue line is straight and tangent to the arc at co-ordinates 900, 103.202.

tomtomtom1 said:
X1= 860, y1= 102.800
x2 = 900, y2 = 103.202

phinds said:
Also, based on the numbers you gave for X1,Y1 and X2, Y2 (which I assume is not X4,Y4), your drawing is massively out of scale so I'm dubious about this actually being a real-world problem.

Your first post would mean (900, 103.202) is (x4,y4) and your second post means it is (x2,y2). You have both phinds and me confused about that. Which is it?

Also, are the two straight lines given ahead of time and the curve has to match their slopes or do you make them tangent to the circle after you are done?
 
  • #10
LCKurtz said:
Also, are the two straight lines given ahead of time and the curve has to match their slopes or do you make them tangent to the circle after you are done?

That's irrelevant. You have 2 points and a radius so the circle is defined. If the lines are to be tangent to the circle, it doesn't matter whether you draw them first or later. In one sense they matter in that they tell you that the defined circle is a specific one of the two that are possible given 2 points and a radius.
 
  • #11
phinds said:
That's irrelevant. You have 2 points and a radius so the circle is defined. If the lines are to be tangent to the circle, it doesn't matter whether you draw them first or later. In one sense they matter in that they tell you that the defined circle is a specific one of the two that are possible given 2 points and a radius.

Yes, I am aware of that. But I don't know if the OP is, and I don't know if he has given all the pertinent information. For all we know, he may have data inconsistent with the arc actually being a circle, even though he has specified a circle (after being asked). Given that he is setting out an arc for a wall, I would doubt that the direction of the wall is arbitrarily determined by the arc. And, for that matter, maybe the wall doesn't really have to be literally tangent to the arc.
 
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  • #12
@tomtomtom1: Is this a real world construction site problem where you have the two walls specified and need to lay out a chalk line for the arc between them?
 
  • #13
LCKurtz said:
Yes, I am aware of that. But I don't know if the OP is, and I don't know if he has given all the pertinent information. For all we know, he may have data inconsistent with the arc actually being a circle, even though he has specified a circle (after being asked). Given that he is setting out an arc for a wall, I would doubt that the directions of the wall is arbitrarily determined by the arc. And, for that matter, maybe the wall doesn't really have to be literally tangent to the arc.

Reasonable point.
 

1. What is the purpose of solving arc problems with given values and coordinates?

The purpose of solving arc problems with given values and coordinates is to determine the properties of an arc, such as its length, central angle, and radius, based on the given information. This can be useful in fields such as engineering, physics, and mathematics, where arcs are commonly used.

2. What are the steps involved in solving an arc problem with given values and coordinates?

The steps involved in solving an arc problem with given values and coordinates may vary depending on the specific problem, but generally they include identifying the given values and coordinates, determining the type of arc (e.g. circular, semicircular, quarter-circle), and using relevant formulas or equations to calculate the desired properties of the arc.

3. Can you solve an arc problem with only some of the given values and coordinates?

It is possible to solve an arc problem with only some of the given values and coordinates, but the result may not be accurate or complete. This is because arcs are geometrically dependent on all of their properties, so having incomplete information may lead to an incorrect solution.

4. What are some common applications of solving arc problems with given values and coordinates?

Solving arc problems with given values and coordinates has various applications in real-world scenarios, such as designing curved structures, calculating the trajectory of a projectile, and determining the circumference of circular objects. It is also commonly used in navigation, astronomy, and computer graphics.

5. Are there any tips or tricks for solving arc problems with given values and coordinates?

Some tips for solving arc problems with given values and coordinates include drawing a diagram to visualize the problem, using the correct formula for the specific type of arc, and double-checking the calculations. It is also helpful to have a good understanding of basic geometry and trigonometry concepts.

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